Details

Time bar (total: 1.6m)

sample263.0ms

Algorithm
intervals
Results
156.0ms621×body80nan
74.0ms345×body80valid

simplify324.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
324.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize42.0ms

Local error

Found 3 expressions with local error:

1.4b
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b
(* n (* 2 PI))
0.2b
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
42×add-sqr-sqrt *-un-lft-identity
33×add-cube-cbrt
26×add-exp-log
22×pow-unpow
18×sqrt-prod
14×pow1
10×add-cbrt-cube
9×prod-exp
8×unpow-prod-down sqr-pow
6×associate-/r* pow-prod-down pow-exp difference-of-squares
5×div-exp associate-/l*
3×expm1-log1p-u pow-pow associate-*l* cbrt-unprod insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp
2×pow-to-exp div-sub div-inv pow-sub
1×cbrt-undiv clear-num frac-2neg associate-*r* *-commutative associate-/l/
Counts
3 → 124
Calls
3 calls:
Slowest
33.0ms
(* n (* 2 PI))
29.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
21.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series581.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
301.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
217.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
62.0ms
(* n (* 2 PI))

simplify26.7s

Counts
124 → 133
Calls
124 calls:
Slowest
758.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
729.0ms
(/ (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
544.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
541.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))
522.0ms
(/ (pow n (/ (- 1 k) 2)) 1)

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

1.4b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
1.4b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.3b
(* n (* 2 PI))
0.3b
(* n (* 2 PI))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
166×add-sqr-sqrt *-un-lft-identity
140×pow-unpow
112×add-cube-cbrt
36×difference-of-squares
26×pow1 add-exp-log
18×distribute-lft-out--
14×add-cbrt-cube
12×pow-prod-down prod-exp
8×div-inv
6×pow-pow associate-*l* pow-exp cbrt-unprod
4×expm1-log1p-u div-sub insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp unpow-prod-down associate-*r* *-commutative pow-sub sqr-pow
Counts
4 → 222
Calls
4 calls:
Slowest
30.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
26.0ms
(* n (* 2 PI))
14.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
14.0ms
(* n (* 2 PI))

series480.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
217.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
165.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
57.0ms
(* n (* 2 PI))
40.0ms
(* n (* 2 PI))

simplify14.7s

Counts
184 → 234
Calls
184 calls:
Slowest
493.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
468.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
459.0ms
(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
431.0ms
(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
412.0ms
(* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))

prune3.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize75.0ms

Local error

Found 4 expressions with local error:

1.4b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
1.4b
(pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))
0.5b
(cbrt (* n (* 2 PI)))
0.5b
(cbrt (* n (* 2 PI)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
164×add-sqr-sqrt *-un-lft-identity
140×pow-unpow
110×add-cube-cbrt
36×difference-of-squares
30×pow1
18×pow-pow distribute-lft-out--
16×add-exp-log
11×pow1/3
9×pow-prod-up
8×pow-prod-down div-inv
6×pow-plus pow-exp prod-exp
4×expm1-log1p-u add-cbrt-cube div-sub insert-posit16 log1p-expm1-u add-log-exp
3×pow-sqr
2×cbrt-prod pow2 pow-to-exp unpow-prod-down pow-sub sqr-pow
1×pow3
Counts
4 → 216
Calls
4 calls:
Slowest
92.0ms
(pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))
30.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
8.0ms
(cbrt (* n (* 2 PI)))
8.0ms
(cbrt (* n (* 2 PI)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
363.0ms
(cbrt (* n (* 2 PI)))
361.0ms
(cbrt (* n (* 2 PI)))
265.0ms
(pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))
208.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))

simplify16.3s

Counts
182 → 228
Calls
182 calls:
Slowest
758.0ms
(pow (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))
524.0ms
(* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
459.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
417.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
414.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))

prune3.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

1.8b
(pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1))
1.4b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.3b
(cbrt (- 1 k))
0.3b
(cbrt (- 1 k))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
106×add-sqr-sqrt *-un-lft-identity
95×pow-unpow
73×add-cube-cbrt
22×difference-of-squares
16×pow1 add-exp-log
12×cbrt-prod
11×distribute-lft-out--
8×div-inv
6×pow-pow pow-prod-down pow-exp prod-exp
4×expm1-log1p-u cbrt-div add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp unpow-prod-down flip3-- pow1/3 div-sub flip-- sqr-pow
1×pow-sub
Counts
4 → 172
Calls
4 calls:
Slowest
26.0ms
(pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1))
21.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
3.0ms
(cbrt (- 1 k))
3.0ms
(cbrt (- 1 k))

series645.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
313.0ms
(pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1))
193.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
73.0ms
(cbrt (- 1 k))
66.0ms
(cbrt (- 1 k))

simplify11.3s

Counts
138 → 184
Calls
138 calls:
Slowest
446.0ms
(- (+ (* 1/9 (* (pow (/ 1 (pow k 4)) 1/3) (* (log (/ 1 n)) (exp (* (- (log (* 2 PI)) (log (/ 1 n))) (pow (pow k 2) 1/3)))))) (+ (* 2/9 (* (pow (/ 1 (pow k 2)) 1/3) (* (pow (log (/ 1 n)) 2) (exp (* (- (log (* 2 PI)) (log (/ 1 n))) (pow (pow k 2) 1/3)))))) (+ (* 2/3 (* (pow (/ 1 k) 1/3) (* (log (/ 1 n)) (exp (* (- (log (* 2 PI)) (log (/ 1 n))) (pow (pow k 2) 1/3)))))) (+ (* 2/9 (* (* (pow (log (* 2 PI)) 2) (exp (* (- (log (* 2 PI)) (log (/ 1 n))) (pow (pow k 2) 1/3)))) (pow (/ 1 (pow k 2)) 1/3))) (exp (* (- (log (* 2 PI)) (log (/ 1 n))) (pow (pow k 2) 1/3))))))) (+ (* 2/3 (* (pow (/ 1 k) 1/3) (* (exp (* (- (log (* 2 PI)) (log (/ 1 n))) (pow (pow k 2) 1/3))) (log (* 2 PI))))) (+ (* 1/9 (* (* (log (* 2 PI)) (exp (* (- (log (* 2 PI)) (log (/ 1 n))) (pow (pow k 2) 1/3)))) (pow (/ 1 (pow k 4)) 1/3))) (+ (* 2/9 (* (pow (/ 1 (pow k 2)) 1/3) (* (log (/ 1 n)) (* (exp (* (- (log (* 2 PI)) (log (/ 1 n))) (pow (pow k 2) 1/3))) (log (* 2 PI)))))) (* 2/9 (* (* (log (* 2 PI)) (* (log (/ 1 n)) (exp (* (- (log (* 2 PI)) (log (/ 1 n))) (pow (pow k 2) 1/3))))) (pow (/ 1 (pow k 2)) 1/3)))))))
446.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
442.0ms
(* (+ (log n) (+ (log 2) (log PI))) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1))
394.0ms
(- (+ (* 1/9 (* (* (log (/ -1 n)) (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (pow (pow k 2) 1/3)))) (pow (/ 1 (pow k 4)) 1/3))) (+ (* 2/9 (* (* (pow (log (/ -1 n)) 2) (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (pow (pow k 2) 1/3)))) (pow (/ 1 (pow k 2)) 1/3))) (+ (* 2/9 (* (* (pow (log (* -2 PI)) 2) (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (pow (pow k 2) 1/3)))) (pow (/ 1 (pow k 2)) 1/3))) (+ (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (pow (pow k 2) 1/3))) (* 2/3 (* (* (log (/ -1 n)) (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (pow (pow k 2) 1/3)))) (pow (/ 1 k) 1/3))))))) (+ (* 1/9 (* (* (log (* -2 PI)) (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (pow (pow k 2) 1/3)))) (pow (/ 1 (pow k 4)) 1/3))) (+ (* 2/3 (* (pow (/ 1 k) 1/3) (* (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (pow (pow k 2) 1/3))) (log (* -2 PI))))) (+ (* 2/9 (* (* (log (* -2 PI)) (* (log (/ -1 n)) (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (pow (pow k 2) 1/3))))) (pow (/ 1 (pow k 2)) 1/3))) (* 2/9 (* (pow (/ 1 (pow k 2)) 1/3) (* (log (/ -1 n)) (* (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (pow (pow k 2) 1/3))) (log (* -2 PI))))))))))
393.0ms
(pow n (/ (/ (- 1 k) 2) 2))

prune3.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes165.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch6.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
3.9s20678×body80nan
3.0s11986×body80valid